An Improved Empirical Equation for Uniaxial Soil Compression for a Wide Range of Applied Stresses
D. D. Fritton* ABSTRACT
The response of soil to compaction forces is nonlinear and not completely described by existing statistical equations. The objective of this study was to find a better empirical equation for uniaxial soil compression. Disturbed and undisturbed samples from three to fivehorizons of four soils, and from soil mixed with four different amounts of sand, were subjected to applied stresses ranging from 0 to 2971 kPa at one to four initial water contents. Data from individual samples representing the three resulting curve shapes were used to evaluate existing and new empirical equations. A new equation was found that fit all three curve shapes better than any of theexisting equations. The new equation fit data points of representative data sets with an average difference of 0.002 to 0.009 Mg m 3, compared with an average difference for two existing equations of 0.011 to 0.033 and 0.014 to 0.060 Mg m 3. The new equation was then fit to all 120 sets of experimental data, using nonlinear regression procedures. Regression relationships were established between threeparameters that have traditionally been used to characterize soil compression (preconsolidation stress, compression index, and elastic rebound/recompression parameter) and the parameters of the new equation.

been represented by many equations. Koolen and Kuipers (1983) and Gupta and Allmaras (1987) discussed a number of these equations including the logarithmic equation used by Gupta and Larson(1982). The logarithmic equation in not able to fit data at applied stresses less than the preconsolidation stress—the point where the stress exceeds any previously experienced by the soil. Bailey et al. (1986) introduced an equation, ln( ) ln( o) (a b )(1
3

e

c

)

[1]

A

t times, soil compaction significantly reduces crop yield. There is no routine procedure, though, to predictthis effect. The response of soil to an applied stress is an important aspect of this problem. Koolen and Kuipers (1983) conclude that the uniaxial soil-compression test is a sufficient representation of soil compaction for agricultural activities. This work started with the intent of evaluating the relationship between the compression index, a parameter derived from uniaxial soil-compression data,and the clay content reported by Gupta and Larson (1982). The extraction of a compression index from the data, however, required arbitrary decisions due to deviations from linearity between bulk density and applied stress at both the low- and highstress ends of each data set. A better description of uniaxial soil-compression data is needed. It is the purpose of this article to present a newempirical equation for uniaxial soil compression that is capable of fitting soil bulk-density data for the entire range of applied stresses for both disturbed and undisturbed soil at any fixed initial water content. Three material properties used by Kirby (1994), who demonstrated the adequacy of uniaxial soil-compression tests for measuring soil material properties using a critical-state model, can becalculated from the coefficients of the new empirical equation described in this article.

where is soil bulk density (Mg m ) at an applied stress of (kPa), o is the initial soil bulk density (Mg m 3 ), and a, b, and c are empirical parameters that fit compression data at stresses, including zero stress, below the preconsolidation stress. McNabb and Boersma (1993) extended the Bailey et al.(1986) equation to represent multiple soil samples that varied in initial bulk density. McNabb and Boersma (1996) further extended this approach to represent multiple soil samples that varied in initial water content as well as initial bulk density. Assouline et al. (1997) point out that the logarithmic equation and the equations based on the Bailey et al. (1986) equation predict an ever-increasing...

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